Prestressed Concrete Structures Multiple Choice Questions on “Deflections of Cracked Members”.

1. Which knowledge is essential to comply with the limit state of deflection?

a) Bending moment

b) Shear stress

c) Shear torsion

d) Load deformation

Answer: d

Clarification: Cracks of limited width are acceptable under occasional overloads or even under working loads according to CED-FIP recommendations and knowledge of the load deformation characteristics of cracked members is essential to comply with the limit state of deflection.

2. The tensile stress of about which limit are invisible to naked eye?

a) 5n/mm^{2}

b) 6n/mm^{2}

c) 3n/mm^{2}

d) 10n/mm^{2}

Answer: c

Clarification: Experimental investigations have shown that micro cracks develop at a tensile stress of about 3n/mm^{2} which is invisible to the naked eye, on further loading cracks are first visible at flexural tensile stresses between 3.5 and 7n/mm^{2} the higher values generally correspond to beams with well bonded steel distributed close to the tensile face as in the case of pretensioned members.

3. The load deflection curve is approximately linear up to stage of __________

a) Invisible cracking

b) Visible cracking

c) Invisible deflection

d) Visible deflection

Answer: b

Clarification: The load deflection curve is approximately linear up to the stage of visible cracking, but beyond this stage the deflections increase at a faster rate due to the reduced stiffness of the beam, if the beam is sufficiently loads, tensile stresses develop in the soffit and when this exceeds the tensile strength of concrete, cracks are likely to develop in the member.

4. In post cracking stage, the behavior of the beam is similar to __________

a) Prestressed concrete members

b) Reinforced concrete members

c) Chemical concrete members

d) Biological concrete members

Answer: c

Clarification: In the post cracking stage, the behavior of the beam is similar to that of reinforced concrete members, the instantaneous deflections in post cracking stage is obtained as the sum of the deflections up to the cracking load based on gross section and beyond the cracking load considering the cracking section.

5. The deflections of cracked structural concrete members may be estimated by __________

a) Unilinear method

b) Matrix method

c) Step method

d) Elongation method

Answer: a

Clarification: The deflection of cracked structural concrete members may be estimated by the Unilinear or bilinear method recommended by the European concrete committee, the slope of first line corresponding to the stiffness of the uncracked section and slope of the second line to that of the cracked section.

6. Which of the following equation is used to compute deflections of unilinear method?

a) βL^{2}e/E_{c}I_{t}

b) βL^{2}M/E_{c}I_{t}

c) βL^{3}/E_{c}R

d) βL^{4}/E_{c}R_{t}

Answer: b

Clarification: The revised American code considers the bilinear character of the load deflection characteristics by incorporating a suitable effective value of the flexural rigidity in the unilinear formula, In the Unilinear method, the deflections are computed by a simple equation of the form

A = βL^{2}M/E_{c}I_{t}, a = maximum deflection, L = effective span, M = maximum moment in the beam, E_{c} = modulus of elasticity of concrete, I_{c} = second moment of area equivalent cracked moment, β = constant.

7. The actual load deflection behavior is possible by assuming __________

a) Bilinear moment curvature

b) Multilinear moment

c) Trilinear moment curvature

d) Bin linear moment curvature

Answer: a

Clarification: In the bilinear method recommended by the 1963 European concrete Committee the moment curvature is approximated by two straight lines, Experimental investigations have shown that a closer approximation to the actual load deflection behavior is possible by assuming bilinear moment curvature relationships.

8. The British code recommended for long time deflection of cracked members is __________

a) BS: 2150-1970

b) BS: 2150-1970

c) BS: 2150-1970

d) BS: 2150-1970

Answer: b

Clarification: The British code BS: 8110-1935 recommendations are comprehensive in this regard, as they incorporate the use of curvature of cracked sections, including the effect of shrinkage and creep in computing long term deflections.

9. The additional long term deflection resulting from creep and shrinkage of flexural members is determined by multiplying the deflection caused by __________

a) Effective load

b) Compressive load

c) Tensile load

d) Sustained load

Answer: d

Clarification: According to ACI: 318-1989 uses a similar approach whereby an additional long term deflection resulting from creep and shrinkage of flexural members is determined by multiplying the immediate deflection caused by the sustained load.

10. The equation for long term deflection of cracked members is __________

a) ξ/1+50ρ’

b) π/1+50ρ’

c) σ/1+50ρ’

d) e/1+50ρ’

Answer: a

Clarification: The prediction of time dependant deflections is complicated in the case of cracked members due to the redistribution of flexural stresses, according to Neville an exact solution results in nonlinear integral equations for which no closed solution is available is λ = ξ/1+50ρ’

ρ’ = (A’_{s}/bd) at midspan, A’_{s} = area of compression reinforcement, b = width of the section, d = effective depth, ξ = time dependent factor.